We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Approximation of a Reifenberg-flat set by a smooth surface.
- Authors
David, Guy
- Abstract
We show that if the set E ⊂ ℝn is well approximated at the scale r0 by planes of dimension d, we can find a smooth surface Σ0 of dimension d which is close to E at the scale r0. When E is a Reifenberg flat set, this allows us to apply a result of G. David and T. Toro [Memoirs of the AMS 215 (2012), 1012], and get a bi-Hölder homeomorphism of ℝn that sends Σ0 to E. If in addition d = n -1 and E is compact and connected, then Σ0 is orientable, and ℝn ∖ E has exactly two connected components, which we can approximate from the inside by smooth domains.
- Subjects
APPROXIMATION theory; SET theory; HOMEOMORPHISMS; INTEGRAL domains; MATHEMATICAL research
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2014, Vol 21, Issue 2, p319
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/bbms/1400592628